Find the term independent of x in the expansion of (i) `[sqrt(x/3)+sqrt(3)/(2x^2)]^10 (ii) [1/2x^(1//3)+x^(-1//5)]^8`

Options

A. 1
B. `5/12`
C. `""^(10)C_(1)`
D. Non of these

Explanation

General term in the expansion is
`""^(10)C_(r)(x/3)^(r/2)(3/(2x^2))^((10-r)/2)=""^10C_(r)X^((3r)/2-10).(3^(5-r))/(2^((10-r)/(2)))` For constant term `,(3r)/(2)= 10 rArr r = (20)/(3)`
Which is not an interger .Therfore , there will be no constant term,